Learning From Errors in Mathematics Classrooms: Development Over Two Years in Dependence on Perceived Error Climate

• In Event: Being Wrong (Sometimes): How Students’ Classroom Assessment Mistakes and Learning Errors Enhance Learning and Motivation

Abstract

Errors elicited from both formative and summative classroom assessments may provide informative feedback on knowledge gaps or misconceptions, and thus exhibit a high potential for learning gains (Zhao, 2011). Adaptive reactions encompass maintaining motivation and initiating learning activities to overcome the errors—theoretically, these reactions are closely related with ideal-typical self-regulated learning (Winne & Hadwin, 1998). However, it is well documented that many students are demotivated by errors and make little out of the immanent learning opportunities (e.g., Author, 2017). A large body of research addressing different patterns following failure identified a series of personal determinants that also predict reactions to errors (for an overview see Schunk, Pintrich & Meece, 2013). In contrast, little is known regarding development and contextual and/or instructional conditions of students’ more or less adaptive reactions to errors—although this would be of particular interest with regard to educational practice. The concept of perceived error climate was suggested to describe such contextual differences (Oser & Spychiger, 2005; Author, 20013; see also Van Dyck, Frese, Baer & Sonnentag, 2005). Error climate is assumed to consist of various facets, e.g. teachers’ tolerance towards errors or his/her support following errors. Until now, only cross-sectional evidence exists that supports the notion that a positive error climate in the classroom is positively associated with adaptive individual reaction to errors.
The present work thus addresses two questions: (a) How does the individual dealing of students with their errors develop over time? (b) Which role plays the classroom context in general and the perceived error climate in the classroom in particular for this development?

Data from a 2-year longitudinal study with five measurement points over the 5th and the 6th grade in academic secondary schools were analyzed. The sample consisted of 1,440 students (51% female) in 69 Mathematics classrooms from 25 schools. Perceived error climate in the classroom was assessed via students’ shared perceptions using an established scale (Author, 2013). Students’ individual reactions to errors were also assessed with a well-validated instrument (Author, 2017).

Confirmatory two-level factorial analyses supported the supposed dimensional structure of perceived error climate, encompassing eight first-order facets and one homogenous second-order factor (see Author, 2013). Growth curve modelling indicated—on average—a negative development of students’ individual reactions to errors over time. This development varied substantially between classrooms and depended systematically from perceived error climate. The more positive the error climate in the classroom was, the less accelerated was the negative development of students’ individual dealing with errors in the subject of Mathematics.

The present results imply a strong need to support students in developing and maintaining adaptive reactions to their errors. They also allow for the optimistic conclusion that teachers can succeed here by means of realizing a positive error climate in class. Practical implications regarding specific instructional practices to achieve this can be derived from the various sub-facets of the error climate concept (see also Oser & Spychiger, 2005).

Authors

• Markus Dresel, Augsburg University

• Gabriele Steuer, University of Augsburg